You can use multiple negative lookbehinds to do what you want. Although I imagine fellow monks will probably have a more elegant solution.

use strict;
use warnings;

for ( <DATA> )
{
        my $variable = qr/(?<!mild\s)(?<!moderate\s)active/;
        print $_ if ( m/$variable/ );
}

__DATA__
foo active
mild active
moderate active
active
[download]

Outputs

foo active
active
[download]